Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer: Volume 2: Hope and Disillusion

Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the development of mathematics and in wider Dutch history. A mathematical genius with strong mystical and philosophical leanings, he advocated the intuitionist view of mathematics and science as a constructive mental activity. This drew him into a discussion with David Hilbert, the leading advocate of the formalist school, about the nature of mathematics, a debate which made Brouwer a legend during his lifetime. He also contributed significantly to research in topology, and was a member of the socio- linguistic Signific Circle. As well as his diverse mathematical interests he had a great impact in wider Dutch society. His keen sense of justice made him a party in many conflicts, both scientific and political. He would often be involved in controversial issues, such as the campaign to undo the boycott of German scientists, and this made him a figure both of admiration and embarrassment in his native Holland. Contents......Page 10 12.1 The two Russians......Page 12 12.2 The definition of dimension......Page 15 12.3 The Viennese connection......Page 38 12.4 The scientific legacy of Urysohn......Page 41 13.1 The first skirmishes in the foundational conflict......Page 52 13.2 Consolidation and entrenchment......Page 64 13.3 The Riemann volume......Page 74 13.4 International relations......Page 79 13.5 The Dutch topological school......Page 85 14.1 More intuitionism......Page 109 14.2 Feelings of crisis and German science......Page 111 14.3 The Berlin lectures......Page 115 14.4 The Vienna lectures......Page 132 14.5 Other activities......Page 140 15.1 The Grundlagenstreit......Page 144 15.2 The Bologna conference......Page 158 15.3 The war of the frogs and the mice......Page 170 15.4 The endings of the Grundlagenstreit......Page 207 15.5 The Menger conflict......Page 214 16 The Thirties......Page 243 16.1 Freudenthal arrives......Page 244 16.2 Intuitionistic logic......Page 247 16.3 The Sodalitas affair......Page 249 16.4 Göttingen's fate under the Nazi's......Page 264 16.5 Bieberbach's conversion......Page 266 16.6 Compositio Mathematica......Page 274 16.7 Göttingen reconsidered?......Page 281 16.8 Dutch affairs......Page 286 17.1 Occupied Holland......Page 309 17.2 Weitzenböck's choice......Page 311 17.3 Freudenthal dismissed......Page 313 17.4 University—resistance or survival......Page 317 17.5 Freudenthal's fortunes......Page 322 17.6 The declaration of loyalty......Page 330 17.7 The Brouwer family in wartime......Page 341 17.8 Weitzenböck in uniform......Page 345 18.1 Purging the university......Page 348 18.2 Faculty politics......Page 370 18.3 Back to research......Page 385 18.4 The loss of Compositio Mathematica......Page 404 18.5 Rearguard actions......Page 417 19.1 The traveller......Page 431 19.2 The pharmacy......Page 458 19.3 The last years......Page 466 19.4 Epilogue......Page 478 20.2 Correspondence and Archives......Page 484 20.3 Chronology......Page 488 References......Page 491 B......Page 506 C......Page 508 E......Page 509 G......Page 510 H......Page 511 K......Page 512 M......Page 513 P......Page 514 S......Page 515 V......Page 516 Z......Page 517 Contents 10 12 The Fathers of Dimension 12 12.1 The two Russians 12 12.2 The definition of dimension 15 12.3 The Viennese connection 38 12.4 The scientific legacy of Urysohn 41 13 Progress, recognition, and frictions 52 13.1 The first skirmishes in the foundational conflict 52 13.2 Consolidation and entrenchment 64 13.3 The Riemann volume 74 13.4 International relations 79 13.5 The Dutch topological school 85 14 From Berlin to Vienna 109 14.1 More intuitionism 109 14.2 Feelings of crisis and German science 111 14.3 The Berlin lectures 115 14.4 The Vienna lectures 132 14.5 Other activities 140 15 The three Battles 144 15.1 The Grundlagenstreit 144 15.2 The Bologna conference 158 15.3 The war of the frogs and the mice 170 15.4 The endings of the Grundlagenstreit 207 15.5 The Menger conflict 214 16 The Thirties 243 16.1 Freudenthal arrives 244 16.2 Intuitionistic logic 247 16.3 The Sodalitas affair 249 16.4 Göttingen's fate under the Nazi's 264 16.5 Bieberbach's conversion 266 16.6 Compositio Mathematica 274 16.7 Göttingen reconsidered? 281 16.8 Dutch affairs 286 17 War and Occupation 309 17.1 Occupied Holland 309 17.2 Weitzenböck's choice 311 17.3 Freudenthal dismissed 313 17.4 University—resistance or survival 317 17.5 Freudenthal's fortunes 322 17.6 The declaration of loyalty 330 17.7 The Brouwer family in wartime 341 17.8 Weitzenböck in uniform 345 18 Postwar Events 348 18.1 Purging the university 348 18.2 Faculty politics 370 18.3 Back to research 385 18.4 The loss of Compositio Mathematica 404 18.5 Rearguard actions 417 19 The restless Emeritus 431 19.1 The traveller 431 19.2 The pharmacy 458 19.3 The last years 466 19.4 Epilogue 478 20 Appendix 484 20.1 Dissertations under supervision of Brouwer 484 20.2 Correspondence and Archives 484 20.3 Chronology 488 References 491 Index 506 A 506 B 506 C 508 D 509 E 509 F 510 G 510 H 511 I 512 J 512 K 512 L 513 M 513 N 514 O 514 P 514 Q 515 R 515 S 515 T 516 U 516 V 516 W 517 Y 517 Z 517
Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the development of mathematics and in wider Dutch history. A mathematical genius with strong mystical and philosophical leanings, he advocated the intuitionist view of mathematics and science as a constructive mental activity. This drew him into a discussion with David Hilbert, the leading advocate of the formalist school, about the nature of mathematics, a debate which made Brouwer a legend during his lifetime. He also contributed significantly to research in topology, and was a member of the socio-linguistic Signific Circle. As well as his diverse mathematical interests he had a great impact in wider Dutch society. His keen sense of justice made him a party in many conflicts, both scientific and political. He would often be involved in controversial issues, such as the campaign to undo the boycott of German scientists, and this made him a figure both of admiration and embarrassment in his native Holland. Although his abilities won him offers from prestigious universities such as Berlin and Gottingen, he preferred to stay in Amsterdam, so that he could pursue a life of quiet unconventionality in the artist community at Laren. This book, the second in a two-volume set, provides a sophisticated analysis of this crucial era of mathematical research, but also gives an important insight into the wider life of one of the most fascinating characters involved. v. 1. The dawning revolution v. 2. Hope and disillusion.